This Bible belonged to the 4th George Emlen (George—>George—>George, b. 1741, d. 1812). It was printed by "John Adams and William Hancock for Mathew Carey" in Philadelphia in 1803. All of George's children were born prior to 1800, so most (if not all) of the family information written in it was done so several years after the fact.
The Bible was sold at auction in 2013 by National Book Auctions to a private collector for $250. You can still view photos and a description at Invaluable.com. One of the photos is of a page of family records, which I have attempted to transcribe below. The photo shows at least one more page of family records behind that one. An attempt to obtain high-resolution images of the family record pages from the buyer (communicating via the auction house) was unsuccessful.
Geo Emlen Son of Geo & Ann Emlen was born the
8th day of March 1741
Sarah Fishbourne / was born the 11th September
1755 / daughter of William & Mary Fishbourne
Geo Emlen and Sarah Fishbourne were Married
at Pine Street Meeting House the 1st February 1775
Mary Emlen their first daughter was born the 28th November
1775, a third day 12 O'Clock at Noon, And departed
this Life on fourth day the 20th August 1777,
Ann Emlen their Second Daughter, was born the 6th
day of June 1777, at 4 O'Clock Afternoon
Elizabeth Emlen was born the 25th October 1778, 10 O'Clock
Sarah Emlen was born the 22nd January 1780, at 10 O'Clock
Geo Emlen was born the 25th Septem'r 1781, at 3 O'Clock A.M.
And departed this Life the 9th August 1782.
William Emlen was born 7th June 1783, at 4 O'Clock A.M.
And departed this Life the 25th day of the Same Month.
Geo Emlen was born the 2nd day of September 1784, at 11 O'
Clock at Night.
Wm. Emlen was born the 30th May 1787, at 1 O'Clock
Sarah Emlen Departed this Life the 28th day
of June, about 3 O'Clock Afternoon 1787.